So I've finally adquired Sony Trinitron CRT (and for free!). The model is KV-21R1E. It was working great, with the exception of some loose soldering in the SCART pins that I had to take care of.
After connecting my PS2 with my retro RGB SCART cable and turning my new TV on, I noticed the picture had an amazing quality but it was off centered horizontally.
I was lucky enough that it came with the original remote, so after a bit of digging through forums and videos I was able to access the Service Menu, pressing the following 4 button combination, with the TV on standby mode:
(i+) , (5) , (VOL+) , ( ) (the one above 1)
So after the TV turns itself on, I get to a screen with the following green text, on top:
60 M EW TT - -

I quickly realized that I could also access the Service Menu itself, by pressing the (MENU) button, and a menu would appear, with the following text on the top:
BE5 V 41 180996 (I think this is the chassis?)
Adjustment 0-63
On the right, it has 3 lines of text, in yellow, like so:
BM = 106
H/M = 000
M/L = 001
I have no idea what these are.

The menu consists of 20 lines each with a different adjustable parameter. I didn't take a picture or write down the default values before changing some of them, and even after resetting, they don't go back to the factory settings, but that doesn't matter, because I didn't mess around with any color or other important values.
VER. SIZE 43 (00-63) - stretches or compresses picture vertically, ruinning aspect ratio
VER. BREATH 15 (00-63) - also seems to stretch and compress picture vertically, but at a much more precise scale
PIN AMPL 11 (00-63) - brings corners in or out
PAR TILT 35 (00-63) - tilts picture on a horizontal axis
V. LINEAR 40 (00-63) - stretches picture vertically, but on different parts of the screen
CORN CORR. 04 - (00-63) - brings corners in or out, but at a much precise scale
H. AMPLIT. 35 (00-63) - stretches or compresses picture horizontally, ruinning aspect ratio
V. POSITION 05 (00-63) - slowly moves picture up and down, flickering with every changing position
H. PHASE 39 (00-63) - moves picture left and right
BLUE 23 (00-63) - more/less blue color
GREEN 25 (00-63) - more/less green color
RED 40 (00-63) - more/less red color
HVBLK1 00 (00-63) - no idea what this does
HVBLK2 00 (00-63) - no idea what this does
V. CENTER 40 (00-63) - no idea what this does
CONC_CT =7 - can't be changed
ST_DT (AUTOMATICALLY FLUCTUATES BETWEEN 252 AND 007) - can't be changed
ZWEI_MAX 36 (ZWEI_MIN-80) - no idea what this does
ZWEI_MIN 18 (0-80) - no idea what this does
ZWEI_TIME 20 (00-I5) - no idea what this does
Pressing (MENU) or ( ) again would bring me back to the Service Menu home menu:
60 M EW TT - -
Now, I found out that you can input any 2 digit combination by pressing the buttons 0-9 on the remote, and the lines after the TT would fill in with the command you input. Not every single one of the 99 combinations work, as far as I was able to discover. Here is what I found out so far:
00 - exit Service Menu and save changes
01 - 100% contrast
02 - 0% contrast
03 - 25% volume
04 - 50% volume
05 - 75% volume
06 - 100% volume
07 - freezes??? (unfreezes with ( ) button).
08 - reset and exit (doesn't reset values from the MENU above but it resets contrast, brightness, etc)
15 - 80% contrast (default)
16 - brightness high (toggle with 40)
17 - toggles between M (default) or "no M" (on the menu above. I have no idea what the M stands for)
19 - toggles between "no P" (default) or P (on the menu above, the P appears bewteen "60" and "M", and I have no idea what it stands for)
22 - the number 22 just stays there and does nothing... (next input combination will already have a 0 as the first digit)
23 - 0% contrast (same as 02 - at least I see no difference) and (next input combination will already have a 0 as the first digit)
24 - BW (no idea what this does)
25 - EW (default) (no idea what this does)
26 - UW (no idea what this does)
27 - LW (no idea what this does)
28 - AW (this turns on P (19) automatically) (no idea what this does)
29 - KW (no idea what this does)
30 - DW (no idea what this does)
32 - 50% contrast
36 - mute (can't unmute from the menu)
37 - exit Service Menu (without saving, I think)
38 - weird symbol with a white up arrow on the left blinking and a white down arrow on the right standing still (no idea what this does)
40 - brightness low (default) (toggle with 16)
50 - green menu text moves vertically
51 - toggles between 60 (default) and 100 (is this the frequency???)
55 - green menu text moves to the left
66 - green menu text moves to the right
77 - toggles between xE or xW (default), where x is B, E (default), U, L, A, K or D (no idea what this means)
I actually use the default low brightness (40) which you can then fine tune with the TV standard menu.
I also toggle between the default 80% contrast (15) and 100% contrast (01), depending on the game. You can also fine tune this with the TV standard menu.
Would really love to hear feedback from you guys. I have no idea what some of these do. And also are there any other combinations that change anything?
Also, is there a way of calculating the relative values of VER. SIZE and H. AMPLIT. for obtaining a perfect 4:3 ratio, but with a picture stretched out to fit the TV screen? I've tried changing both and adjusting just from what looks right, but I was hoping there was some way of calculating one value after you have the other for a true 4:3.
All help is highly appreciated.
Thank you very much
Diogo